Non-local symmetries of first-order equations

It is shown how one can transform scalar first-order ordinarydifferential equations which admit non-local symmetries of theexponential type to integrable equations admitting canonicalexponential non-local symmetries. As examples we invoke theAbel equation of the second kind, the Riccati equation and naturalgeneralizations of these. Moreover, our method describes howa double reduction of order for a second-order ordinary differentialequation which admits a two-dimensional Lie algebra of generatorsof point symmetries can be affected if the second-order equationis first reduced in order once by a symmetry which does notspan an ideal of the two-dimensional Lie algebra.     

Cumulative and continuous laser vaporization synthesis of single wall carbon nanotubes and nanohorns

The conditions for the scaled synthesis of single wall carbon nanotubes (SWNTs) and single wall carbon nanohorns (SWNHs) by laser vaporization at high temperatures are investigated and compared using in situ diagnostics. An industrial Nd:YAG laser (600 W, 1–500 Hz repetition rate) with tunable pulse widths (0.5–50 ms) is utilized to explore conditions for high-yield production. High-speed videography (50000 frames/s) of the laser plume and pyrometry of the target surface are correlated with ex situ high resolution transmission electron microscopy analysis of the products for pure carbon targets and carbon/catalyst targets to understand the effects of the processing conditions on the resulting nanostructures. Carbon is shown to self-assemble into single-wall nanohorn structures at rates of ∼1 nm/ms, which is comparable to the catalyst-assisted SWNT growth rates. Two regimes of laser ablation, cumulative ablation by multiple pulses and continuous ablation by individual pulses, were explored. Cumulative ablation with spatially overlapping 0.5-ms pulses is favorable for the high yield and production rate of SWNTs at ∼6 g/h while continuous ablation by individual long laser pulses (∼20 ms) at high temperatures results in the highest yield of SWNHs at ∼10 g/h. Adjustment of the laser pulse width is shown to control SWNH morphology.     

Altering the catalytic activity of thin metal catalyst films for controlled growth of chemical vapor deposited vertically aligned carbon nanotube arrays

The growth rate and terminal length of vertically aligned carbon nanotube arrays (VANTAs) grown by chemical vapor deposition have been dramatically improved through pulsed KrF excimer laser pretreatments of multilayer metal catalyst films. Silicon wafers coated with Al, Mo, and Fe layers were laser processed in air with single laser shots of varying fluence through circular apertures, then heated to ∼750°C and exposed to acetylene and ferrocene containing gas mixtures typically used to grow vertically aligned nanotube arrays. In situ videography was used to record the growth kinetics of the nanotube arrays in both patterned and unpatterned regions to understand the changes in catalytic activity, growth rates, and termination of growth. The height of the patterned regions varied with fluence, with the most successful treatment resulting in 1.4 cm tall posts of nanotubes embedded in a 0.4 cm tall nanotube carpet. High-resolution transmission electron microscopy images from the nanotubes in the posts revealed fewer walls, smaller diameters, and a much narrower distribution of diameters compared to the nanotubes grown in the carpet. This information, along with data obtained from weighing the material from each region, suggests that pulsed laser processing can also significantly increase the areal density of VANTAs. Research sponsored by the Division of Materials Sciences and Engineering, U.S. Department of Energy.     

Electro-elastic interactions and second order anisotropic constitutive equations

Piezoelectricity is usually expressed as an interaction between mechanical and electrical variables. The physics involved is hence governed by a coupling between Maxwell's equations of electromagnetism and the equations of elasticity. Such a coupling takes us through the piezoelectric constitutive relations. In this work, the second order anisotropic constitutive equations are treated, and in particular, the number of independent material constants is computed for all the 32 crystallographic classes.Paper presented, in reduced version, at the 12th Italian National Congress of Theoretical and Applied Mechanics (AIMETA '95), October 1995, Naples, Italy.     

Multiple-photon ir excitation of electronic states of OsO4 molecule

Basic experimental characteristics of collisionless luminescence of OsO₄ molecule excited by pulsed ir laser radiation are presented. The theoretical model of the process is developed and a comparison with experiment is carried out both for one-frequency and two-frequency ir excitation. From such comparison information is obtained on the fraction of molecules excited by laser radiation as well as on the spectroscopic characteristics of highly excited states.     

Transition to Chaos in the Floating Half Zone Convection

The transition process from steady convection to chaos is experimentally studied in thermocapillary convections of floating half zone. The onset of temperature oscillations in the liquid bridge of floating half zone and further transitions of the temporal convective behaviour are detected by measuring the temperature in the liquid bridge. The fast Fourier transform reveals the frequency and amplitude characteristics of the flow transition. The experimental results indicate the existence of a sequence of period-doubling bifurcations that culminate in chaos. The measured Feigenbaum numbers are δ2 =4.69 and δ4 = 4.6, which are comparable with the theoretical asymptotic value δ=4.669.     

Controllable Growth of Perovskite Films by Room‐Temperature Air Exposure for Efficient Planar Heterojunction Photovoltaic Cells

A two‐step solution processing approach has been established to grow void‐free perovskite films for low‐cost high‐performance planar heterojunction photovoltaic devices. A high‐temperature thermal annealing treatment was applied to drive the diffusion of CH₃NH₃I precursor molecules into a compact PbI₂ layer to form perovskite films. However, thermal annealing for extended periods led to degraded device performance owing to the defects generated by decomposition of perovskite into PbI₂. A controllable layer‐by‐layer spin‐coating method was used to grow “bilayer” CH₃NH₃I/PbI₂ films, and then drive the interdiffusion between PbI₂ and CH₃NH₃I layers by a simple air exposure at room temperature for making well‐oriented, highly crystalline perovskite films without thermal annealing. This high degree of crystallinity resulted in a carrier diffusion length of ca. 800 nm and a high device efficiency of 15.6 %, which is comparable to values reported for thermally annealed perovskite films.